# How to find the value of 11 to the 81nd power and the number of digits [Easy]

11 to the 81th power is 2253240236044012487937308538033349567966729852481170503814810577345406584190098644811.

The formula is as follows.

$11^{81}=$
2253240236044012487937308538033349567966729852481170503814810577345406584190098644811

Also, $11^{81}$ has 85 digits.

On this page, I will introduce how to solve $11^{81}$ and how to find the number of digits of $11^{81}$.

This site is created by Dr. Thomsontom labIt operates under the name

## Calculating 11 to the 81th Power

11 to the 81th power is simply 11 multiplied by 81 times.

Basically, the only way to find it is by multiplication.

Then you can use google search.

If you search for "14 to the 21st power" on google here, a calculator will come up and tell you the answer.

As you can see, it takes effort to calculate the power, so sometimes you need to find out how many digits the value of the power is.

Next, let's find the number of digits in $11^{81}$.

## Number of digits in 11 to the 81th power

Calculating $11^{81}$ gives us 85 digits. Calculating the number of digits in 11 to the 81th power

### Find the number of digits in 11 to the 81th power

Let's calculate the common logarithm of 11 to the 81th power.

\begin{eqnarray}
\log_{10}11^{81}&=&81 \log_{10}11\\
&=&81\times 1.0413\cdots\\
&=&84.352
\end{eqnarray}

In other words,
We can say that $11^{81}=10^{84.352}$, so we know that $11^{81}$ has 85 digits.

### How to find the number of digits

To find the number of digits in $11^{81}$, use common logarithms.

By using the common logarithm, we can calculate the power of 10, so we know the number of digits.

For example, $10^1=10$ is 2 digits.
On the other hand, $10^2=100$, so 3 digits.

So $10^a$ has $10+1$ digits.
If $a$ is a decimal, the number of digits is the integer part plus 1.

$a=11.34$ will be 12 digits.

## power size quiz

Q1

Which one is bigger?

$12 ^ 5$

$5^{12}$

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